Witold -

I think that the situation you describe is fairly common.  There are cliques of statisticians who have favorite methods, and will emphasize one positive aspect or negative aspect of a methodology over another to the exclusion of overall good sense in any given situation. 

For example, there may be many good reasons for multiple imputation, but it is not the only viable imputation method.  A friend was an author for a paper that used another method, and their paper was turned down by a well-respected journal because it was controlled by a clique that believed one must always use multiple imputation, regardless.  Their paper was then published by an even more respected journal.  So the difference was just in the reviewers.

When refereeing, I have always tried to be fair and open minded, but I know not everyone tries to do that.  On one occasion, a minor point, to me, was that a certain software was used to implement weighted least squares (WLS) regression, and the referee, 'grasping at straws' apparently to find any reason he/she could to reject a new idea, unbelievably stated that the software used would not do that.  It was a silly, and demonstrably incorrect statement, but apparently one that the editor, who apparently did not consider me in her clique, simply accepted at face value.  She was obviously uninterested anyway, and I was far too busy to fight it.

Many years ago, I worked in hypothesis testing, and saw that p-values were being radically misused on a commonly occurring basis. I was lucky to get a letter to the editor of The American Statistician published, since mine appeared not to be a popular view.  Today it seems that my view has become much more popular, perhaps primarily because it is of practical importance, and results matter.

Another friend had a paper held while someone else was able to publish first. The situation seemed suspicious to me.  The new methodology involved was groundbreaking, and has become somewhat 'famous.' 

So, yes we are all at the "mercy" of capricious, sometimes malicious people and organizations, and their agendas.  It is my belief that those who reach positions of authority in any organization are highly likely to arrive in such positions for the wrong reasons.   Competence and fairness often have far too little to do with anything.  So, yes, one may easily find oneself "...at the mercy of reviewers who could interpret your results in unfavourable way," and perhaps not really care that you have "...a combination of statistical arguments ... to make to defend [your] point of view," no matter how valid your point of view may be. 

Your best hope may be to publish elsewhere, and hope that others who read your work may treat it more fairly.  But "fairness" is not nearly as common as one would hope.

Best wishes - Jim

James -

A massive stone off my chest. I thought I am theonly one struggling with such issues. It is not everything as straightforward as a level of significance for p value. Thank you very much for a detailed answer. 

Regards

Yes this is a possibility and may not be rare as well. Once a reviewer wrote a program to show that my estimates are false(!) to reject my paper. But unfortunately he overlooked a condition that the parameter has to be an positive integer. Later of course I sent my program to him explaining his mistake and thing worked in my favor.

Witold -

If your reviewer was only looking at a p-value, with no type II error analysis or some other kind of sensitivity analysis, then that was/is a mistake on the part of your reviewer. 

 https://www.researchgate.net/publication/262971440_Practical_Interpretation_of_Hypothesis_Tests_-_letter_to_the_editor_-_TAS

Cheers - Jim

PS - Greatings from the snowbound US eastcoast. We can't handle snow!  - There was really no good place in our townhouse parking lot to put it.   :-) 

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